The Extreme Ultraviolet Variability Experiment (EVE) on the Solar Dynamics Observatory obtains extreme-ultraviolet (EUV) spectra of the full-disk Sun at a spectral resolution of ~1 A and cadence of 10 s. Such a spectral resolution would normally be considered to be too low for the reliable determination of electron density (N_e) sensitive emission line intensity ratios, due to blending. However, previous work has shown that a limited number of Fe XXI features in the 90-60 A wavelength region of EVE do provide useful N_e-diagnostics at relatively low flare densities (N_e ~ 10^11-10^12 cm^-3). Here we investigate if additional highly ionised Fe line ratios in the EVE 90-160 A range may be reliably employed as N_e-diagnostics. In particular, the potential for such diagnostics to provide density estimates for high N_e (~10^13 cm^-3) flare plasmas is assessed. Our study employs EVE spectra for X-class flares, combined with observations of highly active late-type stars from the Extreme Ultraviolet Explorer (EUVE) satellite plus experimental data for well-diagnosed tokamak plasmas, both of which are similar in wavelength coverage and spectral resolution to those from EVE. Several ratios are identified in EVE data which yield consistent values of electron density, including Fe XX 113.35/121.85 and Fe XXII 114.41/135.79, with confidence in their reliability as N_e-diagnostics provided by the EUVE and tokamak results. These ratios also allow the determination of density in solar flare plasmas up to values of ~10^13 cm^-3.